Magnetic Resonance Imaging

We have already observed that electric charge is quantized in units of e, as manifested in the cases of the electron and the proton. These objects also have an intrinsic angular momentum, which we call spin. Spin is also quantized: it is only observed in integer multiples of h / 2, where h is Planck's Constant (equal to 6.626 x 10-34 J s; notice that these units are indeed units of angular momentum).

Here, μs is called the spin magnetic moment, gs is the spin gyromagnetic ratio, μB is the Bohr magneton and ms is 1/2 or -1/2 (the spin of the electron divided by h). Of these numbers, only the Bohr magneton has physical units. Its value is

μB = e h / 4 π me

= 9.274 * 10-24 Am2,

where me is the mass of an electron. If we take e, h and me to be natural constants, the measurement of μs is actually a measurement of gs: its value is -2.0023193043617 (B. Odom et al., Physical Review Letters 97, 030801, 2006). This value has a relative error of 7.6 x 10-13, making it the most accurate measurement in science. What is remarkable is that the theoretical prediction for this value is in total agreement!

If the spins are flipped from their orientations of minimum energy to their orientations of maximum energy, the energy of the photon which flips the spin, as well as the energy of the photon lost when the spin flips back, is

| 2 g μN I B |.

The process we have just described is the essence of Magnetic Resonance Imaging (MRI), in which we:

Orient all the nuclear spins in the object (ie., a patient's body) in parallel with a strong magnetic field.

Flip the spins of the nuclei we are interested in locating in the other direction with a strong pulse of radiation of exactly the right frequency.

Listen for the electromagnetic signal (the radiated photons) when the spins relax to their original state; the frequency will identify the isotope.